Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x-5y &= -1 \\ -7x-5y &= 5\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-7x = 5y+5$ Divide both sides by $-7$ to isolate $x$ $x = {-\dfrac{5}{7}y - \dfrac{5}{7}}$ Substitute this expression for $x$ in the first equation. $-4({-\dfrac{5}{7}y - \dfrac{5}{7}}) - 5y = -1$ $\dfrac{20}{7}y + \dfrac{20}{7} - 5y = -1$ Simplify by combining terms, then solve for $y$ $-\dfrac{15}{7}y + \dfrac{20}{7} = -1$ $-\dfrac{15}{7}y = -\dfrac{27}{7}$ $y = \dfrac{9}{5}$ Substitute $\dfrac{9}{5}$ for $y$ in the top equation. $-4x-5( \dfrac{9}{5}) = -1$ $-4x-9 = -1$ $-4x = 8$ $x = -2$ The solution is $\enspace x = -2, \enspace y = \dfrac{9}{5}$.